Optical thickness is the physical thickness multiplied by the index of refraction of a material. Not only is optical thickness important in many applications but also the measurement of optical thickness often must be very accurate. For example, plates used as filters in Fabry-Perot etalons often must have an optical thickness that is accurate to within a few nanometers.
A known technique for optical thickness testing is the so-called transmitted wavefront test, in which the object is placed inside a Fizeau cavity between a transmission flat (TF) and a reference flat (RF). However, high precision measurement of optical thickness of substrates or similar optical structures having two plane-parallel surfaces that are very close to each other (e.g.  less than 1 mm) can be difficult. This measurement is contaminated by unwanted secondary reflections between the object surfaces that produce second and higher order errors. These errors are increasingly difficult to suppress the thinner the sample is.
In general, in one aspect the invention features a method for measuring an optical thickness of a test object. The method includes: interfering a first optical wave front from the test object and a second optical wave front from a reference surface to produce an interference signal; for a selected location on the test object, obtaining an interference pattern of the test object at a first wavelength xcex1; for the selected location, calculating a first estimate of the optical thickness from the interference pattern recorded at wavelength xcex1; for the selected location obtaining an interference pattern of the test object at a second wavelength xcex2; for the selected location, calculating a second estimate of the optical thickness from the interference pattern recorded at wavelength xcex2; and for the selected location, calculating a third estimate of the optical thickness by combining the first and second estimates of optical thickness.
Embodiments of the method may include any one of the following features.
The method may include performing the processes above for each location of a two-dimensional array of locations to generate an estimate of optical thickness for each location of the two-dimensional array of the test object.
The third estimate of the optical thickness may be calculated by averaging the first and second estimates of optical thickness.
The wavelengths xcex1 and xcex2 may be selected so that errors cancel when the first and second estimates of optical thickness are combined.
The wavelength xcex2 may depend on xcex1, an approximate physical thickness of the test object, T, and the index of refraction n of the test object. The wavelength xcex2 may satisfy the relationship xcex2=xcex1xc2x1(2 m+1)xcex12/4nT where m is an integer. Calculating a third estimate of the optical thickness may include averaging the first and second estimates of optical thickness. The processes of the method may be performed for each location of a two-dimensional array of locations to generate an estimate of optical thickness profile for each location of the two-dimensional array of the test object. The first and second optical wavefronts may have a relative phase. An interference pattern may be obtained by: scanning the relative phase of the first and second optical wavefronts over a predetermined range of phase shifts; while scanning the relative phase, monitoring at the selected location, a change in the interference signal as a function of the phase shifting; and storing as the interference pattern the monitored change in the interference signal for the selected location. The test object and the reference surface may have a relative separation and scanning the relative phase of the first and second optical wavefronts may include mechanically changing the separation between the reference surface and the test object. Interfering a first optical wave front from the test object and a second optical wavefront from a reference surface may use a Fizeau interferometer. The third estimate of optical thickness may combine only the first and second estimates of optical thickness.
Finally, in another aspect, the invention may feature a program stored on a computer-readable medium for causing a computer to perform the functions of: obtaining an interference pattern for a selected location on a test object at a first wavelength xcex1; for the selected location, calculating a first estimate of the optical thickness from the interference pattern recorded at wavelength xcex1; for the selected location obtaining an interference pattern of the test object at a second wavelength xcex2; for the selected location, calculating a second estimate of the optical thickness from the interference pattern recorded at wavelength xcex2; and for the selected location, calculating a third estimate of the optical thickness by combining the first and second estimates of optical thickness.
The details of one or more embodiments of the invention are set forth in the accompanying drawings and the description below. Other features, objects, and advantages of the invention will be apparent from the description and drawings, and from the claims.